High Elf Slayer, Khajiit Slayer, and Wood Elf Slayer are awarded for killing members of the Altmer, Khajiit, and Bosmer races, respectively. Members of the Aldmeri Dominion will have the most trouble with these achievements, as there will be far fewer players of those races in the other Alliances. You'll have better luck facing members of your own Alliance's races by participating in Battlegrounds.